Implement Fibonacci

README.md

@@ -1,3 +1,15 @@
-# mit_606_dp
+# MIT 6.006 Introduction to Algorithms
 
-Implementations of some dynamic programing example outlined in the MIT 6.006 "Introduction to Algorithms"
+Implementations of some dynamic programing example outlined in the available material on youtube.
+
+- 2011
+  - [Dynamic Programming I: Fibonacci, Shortest Paths](https://www.youtube.com/watch?v=OQ5jsbhAv_M)
+  - [Dynamic Programming II: Text Justification, Blackjack](https://www.youtube.com/watch?v=ENyox7kNKeY)
+  - [Dynamic Programming III: Parenthesization, Edit Distance, Knapsack](https://www.youtube.com/watch?v=ocZMDMZwhCY)
+  - [Dynamic Programming IV: Guitar Fingering, Tetris, Super Mario Bros.](https://www.youtube.com/watch?v=tp4_UXaVyx8)
+
+- 2020
+  - [Part 1: SRTBOT, Fib, DAGs, Bowling](https://www.youtube.com/watch?v=r4-cftqTcdI)
+  - [Part 2: LCS, LIS, Coins](https://www.youtube.com/watch?v=KLBCUx1is2c)
+  - [Part 3: APSP, Parens, Piano](https://www.youtube.com/watch?v=TDo3r5M1LNo)
+  - [Part 4: Rods, Subset Sum, Pseudopolynomial](https://www.youtube.com/watch?v=i9OAOk0CUQE)

fibonacci.py

@@ -0,0 +1,26 @@
+def fibonacci(n: int):
+    """Return the n-th Fibonacci number."""
+
+    memo: dict[int, int] = {}
+    """The memoization register."""
+
+    def dp(i: int):
+        """Recursive subproblem: return memoized i-th Fibonacci number."""
+
+        # check if memoized yet
+        f = memo.get(i, None)
+        if f is not None:
+            return f
+
+        # compute actual value, making "free" recursive calls
+        f = 2 if i <= 2 else dp(i-1) + dp(i-2)
+
+        # set the memoization register
+        memo[i] = f
+
+        return f
+
+    return dp(n)
+
+
+print(f"The 9th Fibonacci number is: {fibonacci(9)}")